I think that one of the major hurtles of a privately run space organization is the cost. The other is the red tape involved with even starting such an organization. However, the red tape problem can be circumvented. Which still leaves the large problem of funding such a venture. If the founders of such an organization got corporate funding, from as many places as they could, they would probably get enough money to build a space craft of some sorts. Once this new agency had completed its first mission, more corporations would likely be willing to finance a proven agency a mission to mine valuable ore on Mars or set up satellites, if the (let's call it the New Space Agence, or NSA) were able to send the satellite up for less than it would cost a government funded organization. Then comes the problem of pilots. Who would pilot the ships? A separate training facility, maybee based on NASA training, could do it.